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One side of a square makes an angle alph...

One side of a square makes an angle `alpha` with x axis and one vertex of the square is at origin. Prove that the equations of its diagonals are `x(sin alpha+ cos alpha) =y (cosalpha-sinalpha)` or `x(cos alpha-sin alpha) + y (sin alpha + cos alpha) = a`, where a is the length of the side of the square.

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ARIHANT MATHS ENGLISH-THE STRAIGHT LINES-Exercise (Questions Asked In Previous 13 Years Exam)
  1. One side of a square makes an angle alpha with x axis and one vertex o...

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  2. The line parallel to the x-axis and passing through the intersection o...

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  3. A straight line through the point A (3,4) is such that its intercept b...

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  4. The line L1:""y""-""x""=""0 and L2:""2x""+""y""=""0 intersect the line...

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  5. Let P-=(-1,0),Q-=(0,0), "and " R-=(3,3sqrt(3)) " be three points". T...

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  6. The perpendicular bisector of the line segment joining P (1, 4) and...

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  7. The lines p(p^2+1)x-y+q=0 and (p^2+1)^2x+(p^2+1)y+2q=0 are perpendicul...

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  8. The Line L given by (x)/(5) + (y)/(b) =1 passes through the point (13,...

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  9. A straight line L through the point (3,-2) is inclined at an angle 60^...

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  10. The line L1:""y""-""x""=""0 and L2:""2x""+""y""=""0 intersect the line...

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  11. If the line 2x+y=k passes through the point which divides the line seg...

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  12. A ray of light along x+sqrt(3) y = sqrt(3) gets reflected upon reachin...

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  13. For a gt b gt c gt 0, the distance between (1, 1) and the point of int...

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  14. Let P S be the median of the triangle with vertices P(2,2),Q(6,-1)a...

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  15. Let a, b, c and d be non-zero numbers. If the point of intersection of...

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  16. For a point P in the plane, let d(1)(P) " and " d(2)(P) be the distanc...

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  17. The number of points, having both co-ordinates as integers, that lie i...

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  18. Two sides of a rhombus are along the lines x-y+1=0 and 7x-y-5=0. If it...

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